Modal Logics of Space
Guram Bezhanishvili, Johan van Benthem

Abstract:
We survey modal logics of spatial structure in topology, starting from
classical results by Tarski and McKinsey, up to modern techniques in
modal logic, including bisimulation and specially designed extended
modal languages. Work covered includes that of several communities in
Georgia, The Netherlands, the UK, and the US. In addition, we show how
affine and metric geometry, and even mathematical morphology over
vector spaces, can be described with modal logics.